Inswinger and outswinger controversy
= Introduction = NOTE: Some of the numbers (angles and other measurements) need to be updated. Most importantly, the maximum rotation angles are overly optimistic, because stacking prevents reaching the full draw in practice. One of the big controversies surrounding the study of late Roman (usually metal-framed ballistas) is how their arms operate. There have traditionally been two camps: those who claim these metal-framed ballistas were outswingers and those who claim they were inswingers. In an outswinger the arms of the ballista point away from the case and slider in ~80 degree angle before pulling back the bowstring. When the bowstring is pulled back, the tips of the arm rotate inwards, towards the side of the case and slider. In an inswinger the arms initially point towards the target and are pulled back through the field-frame, tips of the arms almost touching each other in the process. As mentioned here, most of existing research leans heavily on interpretation of ambiguous ancient texts and diagrams. The inswinger theories, on the other hand, lean heavily on archaeological finds. = Operating characteristics of an inswinger = If the arms of a ballista are inswinging, they can travel a much wider arc (up to 165 degrees) than in an outswinging configuration (60-70 degrees). In an inswinger, the curved parts of the field-frame bars can be cushioned to stop the arm. Although it would be technically possible to stop the arms of an outswinger similarly, it would not yield any benefits. Therefore the heel pad mentioned by Heron (e.g. Marsden 1971: 29) is used instead. This means that in an inswinger the arm does not have to be pushed as far through the cord bundle, because there's no need for a heel. Interestingly the curved parts of the Gornea field-frames are especially wide. Although this widening does serve other purposes too, it also helps cushioning the blow of the arm effectively. The extra arm travel means that the torsion bundles in an inswinger can store up to 2,5 times the energy of an outswinger if the cord bundle can take it. Also, the bowstring movement characteristics in inswingers and outswingers are quite different. Let's take an inswinger CAD model built according to P.H.'s dimensions as an example: As the arms themselves accelerate for the whole duration of the shot, the bowstring moves forward even faster at the end than the above table would lead us to believe. Apparently (=testing needed) the final phase of arm movement is critical for the velocity of the bolt. However, this rapid acceleration of the string (and bolt) comes at the cost of reducing the leverage of the arms. This means the bolts have to be light to benefit. The general characteristics of the cheiroballistra's arm/bowstring movement are shown in this diagram: Wilkins (2000: 100) claims that in an inswinger the bolt leaves the slider before the arms have moved through their whole arc. His argument is that when the arms are moving outwards (away from the slider) during last half of their travel (in degrees), the forward movement of the string slows down and bolt thus leaves the slider. Wilkins is clearly confused about interaction of the bowstring and the arm as well as basic physics: * The arms accelerate until the pad in the curved field-frame bar stops them * The bowstring's (and thus bolt's) acceleration at any given point depends on ** arm acceleration (at that point) ** the amount of leverage given by arm/bowstring geometry (at that point) * Bowstring and the bolt maintain most of their forward momentum regardless of what the arms are doing. They only lose some momentum through friction and air resistance, to which they are both subject. When looking at the table and diagram above, it's apparent that bowstring movement per unit of arm movement is slowest somewhere between 40 and 60 degrees from rest position. However, there's no phase where the arms move, but the bowstring does not. Even if that was the case as Wilkins (2000: 100) claims, the bolt and bowstring travel together, retaining their momentum. Only if the acceleration of the bowstring suddenly became negative would the bowstring and bolt loose their contact. Of course, this does not happen because of the reasons stated in above list. Wilkins also criticized the inswinger design by claiming that in it the bowstring travels only about half of that allowed by conventional arms (Wilkins 2000: 100). This claim has no basis. Wilkins apparently reached this conclusion by using his s.c. "shortened" (=correct length) arms on the inswinger mock-up and overly long arms on his real, operating outswinger. This obviously allows the outswinger bowstring to be pulled back much further. If same length arms (cone 11d long and hook 1,5d long) are used in both outswinger and inswinger configurations, the inswinger wins by a clear margin: * Inswinger with initial arm angle of 30 degrees from parallel to slider, measured outwards from the slider. 165 degree rotation and bowstring 35,87 dactyls long. Visualized in the picture above. Total bowstring travel 33,36 dactyls. * Outswinger with initial arm angle 16,82 degrees from perpendicular to slider, measured outwards from the slider. 70 degree rotation and bowstring 43,53 dactyls long. Visualized in the picture below. Total bowstring travel 24,16 dactyls. Although 165 degrees is a close to the maximum for an inswinger, so is 70 degrees for an outswinger. Marsden (1971: 231) estimated that an outswinging cheiroballistra would allow 59 degrees of arm travel and Wilkins (2003: 49) managed to increase that to 70 degrees only by rotating the tenons at the ends of the little ladder beams by 18 degrees. It is also possible that Wilkins meant to say that "for given amount of arm rotation inswinger's bowstring moves forward little less than half that of an outswinger's bowstrings". This is of course true, but does not change the fact that inswinger's springs are capable of storing ~2,5 times the energy of an outswinger. Also, widening the inswinger's frame would allow longer draw with same amount of rotation. = Operating characteristics of an outswinger = An outswinger's bowstring accelerates more linearly. This is visualized in this picture: The above cheiroballistra's bowstring/arm travel in numbers: On average the tip of the arm moves ~1,67 dactyls for every 10 degrees of rotation.As the bowstring is pulled back, the pull is initially very smooth but gets stiffer and stiffer. This is what archers call stack and is caused by decrease of leverage from 4:1 (at 0-10 degrees) to 1:1 (at 60-70 degrees). This also means that leverage of the arms upon the bowstring (and bolt) reduces as the bowstring travels forward during launch. The same happens in a much more dramatic fashion with an inswinger (see above). = Case for inswingers = Ancient texts Wilkins (2000: 100) has criticized the inswinging theory on several points. Some of his points have to do with dimensions given by P.H.'s cheiroballistra. First, he claims that the arms of a P.H.'s cheiroballistra have to be shortened or they will clash. This is not true, unless one lengthens the metal hooks of the arms like he did (see Wilkins 1995 & 2003). P.H. states that the "cone-shaped parts" have to be 11 dactyls long (see Marsden 1971: 217; Wilkins 1995: 32). If the field-frames are placed as described here, the center of the cord bundle is 12,8 d away from the center of the ladder (and slider). The arms need to be pushed through the cord bundle and a little beyond, so they project about 10,6 d from the bundle's center, assuming the hooked tips are ~1 d long. This means that when facing each other (perpendicular to the case and slider) the arms are ~4,4 d away from each other. This is more than enough clearance. Also, Iriarte (2003) has argued that all palintones were inswingers, based on other (non-cheiroballistra) artillery treatises. The Hatra ballista The Hatra ballista is probably the most conclusive piece of evidence for inswinger proponents. The thorough description of the find along with a reconstruction was published by Baatz (1977; 1978). The Hatra ballista contained 8 close ended bronze corner fittings. Half of these were "mirrored" but otherwise the same as the other half. The fact that these corner fittings were close-ended means that they could only have been attached to the end of a beam (e.g. a side stanchion). The drawings in Baatz's article clearly show that each corner of the Hatra ballista frame had one of these fittings. Furthermore, Wilkins himself (2003: 68) provides a set of excavation/conservation photos which too make this clear. In a nutshell, there were two vertical side stanchions at each end of the Hatra ballista frame and the bronze corner fittings were attached to their ends. It is very difficult to explain the corner fittings in any other way. This is what effectively forces the Hatra ballista to be an inswinger rather than outswinger. To circumvent this problem (if he was indeed aware of it) Wilkins (2003: 68) moved the inner side stanchion towards the middle of the frame. This allowed him to force the Hatra ballista to fit his outswinger theory at the cost of ignoring the inner corner fittings which had been attached to vertical beams. And if the vertical beams didn't go from bottom to the top, they serve absolutely no purpose. This has previously been pointed out - with different wording - by Iriarte (2003: 115). Iriarte (2003: 116) also rightly criticizes Wilkins' outswinging Hatra ballista for the lack of any (heel) pad for stopping the arms. Unlike in inswingers, the notch in the outer side stanchion could not be used for the purpose, either. This means that the bowstring has to stop the arms and has to be exceedingly strong. He also notes that if Wilkins' reconstruction would take into account the inner side stanchions, the arm could only rotate around 35 degrees, not 78 degrees as Wilkins (2003: 70) claims. I only have to add a few things to this. First, in Wilkins' ballista (2003: 70), the washer is only partially supported by the stanchions. It is very unlike that design such as that could stand the huge compressive forces exerted by the torsion springs, as noted by Iriarte (2003: 115). Second, Wilkins (2003: 70) added additional notches to inner side stanchions to increase arm travel further. Regardless, Iriarte's inswinging Hatra ballista arms could rotate much more (103 degrees), the washers were properly supported and a heel-pad could be used to stop the arms (Iriarte 2003: 116) Other archaeological finds Since Marsden (1971) several field-frames, kamarions and other parts have been found from Gornea, Lyon, Sala and Orsova. It is not possible to use any of the archaeological field-frames for an outswinger, unless one does one of the following: # Assumes the curve in the curved field-frame bar has suddenly changed it's purpose. The purpose of this curve is to allow the arm to recoil further (Heron, Bel. W. 91-93). This route was taken by Baatz (1978: 13; 1999: 14) and initially by Iriarte (2000: 64). Later (2003) Iriarte fixed his interpretation and moved to the "inswinger camp". Marsden (1971: 224) did not have this issue, as he had not seen any archaeological field-frames or their Pi-brackets. # Makes up some solution to explain (and "fix") the location and angle of the Pi-brackets in the field-frames. This route was taken by Wilkins with his locking rings (1995: 36-38; 2003: 49-50). The unsuitability of the archaeological field-frames in the outswinging configuration was also noted by Nick Watts in his blog when he was planning his Orsova reconstruction. His reconstruction has since then become very successful in terms of performance. Although Iriarte (2000: 61-62) already refuted most of the arguments Wilkins made for the locking rings, I feel I got to go a little deeper. One of the problems Wilkins fixed with his locking rings had to do with the vertical placement of the bowstring. He does not state the causes of the issue very clearly, though. He says (1995: 19) the following: "If, for the sake of argument, the ladder Tenons were somehow inserted through the Pittaria, then the Case and Slider would be lifted higher, and to avoid scraping along the Slider the Bowstring would have to be much higher than halfway up Frames 10,5 dactyls high." By "Frames 10,5 dactyls" high he means the total height of the field-frame bars and rings (see below). He discussed this issue further in his "Missing parts" chapter (Wilkins 1995: 34). The problem he had is visualized below; above it is presented a very simple solution to the same problem: Notice the construction of the slider (discussed in detail here) and the level of the bowstring. In the picture below the bowstring is way too low. This of course causes friction which eats away bolt velocity and is generally a bad idea. Why did Wilkins have this issue, then? There are actually two reasons: First, Wilkins assumed that the bars had tenons and counted them as part of their length (10,5 d). This effectively shortened the field frames by 1,5-2 d, depending on how far above the ring the tenons projected before being riveted. The thickness of the field-frame rings also affects this figure. Regardless, this moved Wilkins' bowstring down towards the slider. Why tenons, then? Wilkins' own translation (1995: 17) says "to attach", not "to rivet". Marsden (forcibly?) translates the same verb as "to weld" (1971: 215). Wilkins' main argument is that somehow a welded joint would be too weak (Wilkins 1995: 19), when actually the contrary is true: a proper forge welding produces joints that are as strong as the materials welded together. Also, Wilkins (1995: 19) used the existence of tenons in the bars of the Gornea field-frames as proof of tenons in cheiroballistra field-frame bars. However, the tenons in Gornea field-frames only prove that the Gornea field frames were riveted together. Both welding and riveting would be equally possible for the cheiroballistra, except for the fact that P.H. does not talk about tenons or riveting at all. It's also possible - even likely - that P.H. was describing an assembled machine and simply forgot to mention the extra length needed for tenons. As a summary, Wilkins' shortening of the bars is very risky. Even if Wilkins is correct and the distance between the rings was less that 10,5 d, it does not negatively affect the solution presented in the upper picture above. Second, Wilkins chose to make his slider from two parts, the upper one having the height (1,25 d) stated by P.H. This means that his slider was 1 dactyl higher than if it was made from one piece. Why did he not see the most obvious solution to this problem? To understand this we must not forget that Wilkins (1995; 2000; 2003) had decided beforehand that the cheiroballistra was a winched, outswinging weapon. This left him with little choice but force the sources to fit his expectations. The most likely reason why Wilkins could not use a one-piece slider was it's small size: it is very hard or even impossible to attach winch ropes and a strong triggering mechanism to a slider whose surface is only 0,25 d above the case, 2 d wide at the bottom and ~1,3-1,5 d wide at the top. A slider resting on top of the case is much more convenient in this regard. Apparently even the 2 d wide slider was not strong enough, so Wilkins arbitrarily widened it from 2 d to 2,5 d (Wilkins 1995: 11). In addition to fixing the bowstring issue Wilkins also had to solve the problem with the "curve being in the wrong place" and the issue with "Pi-brackets pointing in the wrong direction". As mentioned, he achieved both goals with his huge bronze locking rings. They allowed him to rotate the entire field-frames ~90 degrees (Wilkins 1995: 38; 2003: 49) and thus make the cheiroballistra fit his outswinger scheme. A reality check is in place here: if he ancients really had wanted cheiroballistra to be an outswinger, they sure could have devised a much simpler solution for solving the problems mentioned above. For example, the could have simply rotated the Pi-brackets 90 degrees and passed the tenons of the ladder and arch through them. It's certain that the Romans were intelligent enough not to bother casting extremely complicated, heavy and costly pieces of bronze to fix every field-frame that was inherently broken by design (for an outswinger, that is). Besides this, there is no archaeological or textual evidence of such field-frames. The only reasonable argument from Wilkins against passing the tenons through the Pi-brackets has to do with dimensions given by P.H. This is discussed in detail in the cheiroballistra article. If Wilkins had not decided beforehand that the cheiroballistra was a winched outswinger, he would not have had any of these problems: * In an inswinger the openings of the Pi-brackets are parallel with little ladder beams and little arch. Thus their tenons can be inserted into the Pi-brackets without any issues. * In an inswinger the curved field-frame bars are naturally in the correct position without any trickery. The alignment of the field-frame bars in an inswinging cheiroballistra is discussed in detail in the cheiroballistra article. = Case for outswingers = Please add, if any. = References = References can be found from the bibliography page. Category:backup Category:Inswinger Category:Outswinger Category:Research Category:Theoretical Category:Cheiroballistra Category:Two-armed torsion engines Category:Arms Category:Bowstring